Question

what is the sum of first 20 terms of an AP., if a=20 and t20= 36?​

Answer 1

Answer:

$t_{20}= 36, \: a = 20, \: n = 20 \\ S_{n} = \frac{n}{2} [a+t _{n} ] \\ S_{20} = \frac{20}{2}[20 + 36 ]\\ S _{20} = 10 \times 56 \\ S_{20} = 560$

Answer 2

Answer:

The sum of the first 20terms of the AP = 560

COMPLETE SOLUTION

Given

First Term (t₁) of the AP = 20

20th Term t₂₀ = 36

To Find

The sum of first 20 terms (S₂₀) of the AP

ANSWER

Sum of n terms of an AP,

$\bigstar \sf S_n = \dfrac{n(t_1+t_n)}{2} \longrightarrow (1)$

Here,

n = 20

$\sf t_n (t_2_0)= 36$

t₁ = 20

On Substituting the above values in (1) , We get

$\sf S_2_0= \dfrac{20(20+36)}{2}$

$\implies$

$\sf S_2_0 = \dfrac{20(56)}{2}$

$\implies$

$\sf S_2_0 = \dfrac{1120}{2}$

$\implies$

$\sf S_2_0 = 560$

$\red\bigstar$ The sum of the first 20 terms of the AP = 560